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fine control of a Groebner basis computation

Sometimes a Groebner basis computation doesn't finish quickly enough. If so then this section might be of use. THIS PAGE IS UNDER CONSTRUCTION.

Partially computed Groebner bases

Suppose that you have computed part of a Groebner basis. For example, you may have interrupted the computation using CTRL-C (typing 'c' while holding the CTRL key down, in emacs, you have to type CTRL-C twice), or you may have given options requesting only partial computation.
i1 : R = ZZ/32003[a..e];
i2 : I = ideal(random(3,R),random(3,R),random(3,R))

                3         2           2         3         2                
o2 = ideal (498a  + 12901a b + 6847a*b  + 14022b  + 10510a c - 12117a*b*c -
     ------------------------------------------------------------------------
          2            2           2        3         2                
     9968b c + 10467a*c  - 15963b*c  + 1331c  - 14639a d + 14748a*b*d -
     ------------------------------------------------------------------------
          2                                 2            2          2  
     5996b d - 189a*c*d - 4743b*c*d - 10539c d + 13098a*d  + 6176b*d  +
     ------------------------------------------------------------------------
             2        3        2                  2                          
     12208c*d  - 6837d  - 1758a e + 10a*b*e + 497b e - 13104a*c*e - 6699b*c*e
     ------------------------------------------------------------------------
             2                                               2           2  
     - 11311c e - 1573a*d*e - 11653b*d*e + 14456c*d*e + 1974d e - 6496a*e  -
     ------------------------------------------------------------------------
             2           2           2         3         3        2   
     15134b*e  + 14640c*e  - 14279d*e  + 12857e , - 6465a  - 2117a b +
     ------------------------------------------------------------------------
             2        3        2                      2           2  
     14162a*b  - 4504b  - 8964a c + 4276a*b*c - 12043b c + 4021a*c  +
     ------------------------------------------------------------------------
            2        3        2                      2               
     5565b*c  + 9384c  - 1077a d + 15062a*b*d - 8045b d - 9652a*c*d -
     ------------------------------------------------------------------------
                      2            2          2          2        3        2 
     7872b*c*d + 8885c d - 12467a*d  + 4614b*d  - 2796c*d  - 5066d  + 7379a e
     ------------------------------------------------------------------------
                         2                                   2               
     - 10167a*b*e - 4104b e - 14200a*c*e - 4939b*c*e - 11132c e - 6504a*d*e +
     ------------------------------------------------------------------------
                                   2           2          2          2  
     1920b*d*e + 10129c*d*e + 4060d e - 9339a*e  + 3134b*e  + 6148c*e  -
     ------------------------------------------------------------------------
             2        3         3        2           2        3        2   
     13334d*e  - 4023e , - 2894a  + 2822a b - 9560a*b  - 1107b  - 9841a c +
     ------------------------------------------------------------------------
                       2            2          2        3         2   
     5048a*b*c - 11201b c + 13114a*c  + 4864b*c  + 5638c  + 13178a d +
     ------------------------------------------------------------------------
                        2                               2            2  
     14103a*b*d + 11989b d + 78a*c*d + 8521b*c*d + 2607c d - 15167a*d  +
     ------------------------------------------------------------------------
             2           2        3         2                      2   
     11335b*d  + 15209c*d  - 3766d  + 12917a e - 1960a*b*e + 14733b e +
     ------------------------------------------------------------------------
                                   2                                        
     2950a*c*e - 10099b*c*e - 9770c e - 1344a*d*e + 12542b*d*e - 5711c*d*e +
     ------------------------------------------------------------------------
           2            2          2          2           2        3
     15906d e - 14192a*e  - 5806b*e  + 6567c*e  + 14887d*e  + 1902e )

o2 : Ideal of R
i3 : gens gb(I,PairLimit=>7);

             1       7
o3 : Matrix R  <--- R
Get the Groebner basis object:
i4 : g = gb(I,StopBeforeComputation => true);
i5 : leadTerm gens g

o5 = | ab2 a2b a3 b3c b4 abc3 a2c3 |

             1       7
o5 : Matrix R  <--- R
We can make a Groebner basis snapshot by using StopBeforeComputation, or gbSnapshot:
i6 : gens gb(I,StopBeforeComputation => true)

o6 = | ab2+9340b3-3772a2c-3993abc-3729b2c-143ac2-470bc2-1066c3+12735a2d-
     ------------------------------------------------------------------------
     15822abd+6849b2d+1473acd-2776bcd-11743c2d+845ad2+15220bd2+12549cd2+
     ------------------------------------------------------------------------
     2978d3+9578a2e+3201abe+6902b2e-11844ace-9562bce-8574c2e+7108ade+13908bde
     ------------------------------------------------------------------------
     +1783cde-2677d2e-15285ae2+2464be2+14683ce2+3054de2-4244e3
     ------------------------------------------------------------------------
     a2b+10749b3-13762a2c-6754abc-14874b2c-3103ac2-11017bc2-861c3+875a2d-
     ------------------------------------------------------------------------
     4515abd-15099b2d+2957acd+961bcd+1307c2d-5566ad2-13997bd2+4381cd2-2137d3-
     ------------------------------------------------------------------------
     13004a2e-13951abe+4821b2e-14880ace-10289bce+1975c2e-12765ade-4213bde-
     ------------------------------------------------------------------------
     3858cde+4660d2e-15265ae2+9028be2+6952ce2+11654de2-6273e3
     ------------------------------------------------------------------------
     a3+7971b3+4695a2c-3947abc-6395b2c-8817ac2+7661bc2+5732c3-15476a2d-
     ------------------------------------------------------------------------
     11912abd-6223b2d+760acd-8330bcd+9909c2d-2032ad2-8782bd2-4532cd2-3206d3+
     ------------------------------------------------------------------------
     4299a2e-14070abe+4621b2e-5398ace-305bce-136c2e+322ade-15399bde+3034cde+
     ------------------------------------------------------------------------
     1881d2e-925ae2-64be2+3314ce2-4292de2-3267e3
     ------------------------------------------------------------------------
     b3c+4967a2c2-2800abc2-5615b2c2+1793ac3-9479bc3+14918c4-10676b3d+
     ------------------------------------------------------------------------
     13812a2cd-5456abcd+15857b2cd+3572ac2d-7642bc2d-7501c3d+4854a2d2-2393abd2
     ------------------------------------------------------------------------
     +13597b2d2+8612acd2-3394bcd2-2725c2d2-14669ad3+2856bd3+1377cd3+6665d4-
     ------------------------------------------------------------------------
     9713b3e+6372a2ce-8012abce+3016b2ce+4632ac2e-761bc2e+10130c3e-14219a2de+
     ------------------------------------------------------------------------
     609abde+3592b2de+5757acde-12653bcde+7173c2de-8779ad2e-5567bd2e+3334cd2e-
     ------------------------------------------------------------------------
     4952d3e-15899a2e2+7884abe2-12387b2e2+7298ace2+11864bce2-13073c2e2-
     ------------------------------------------------------------------------
     8251ade2-11095bde2-10851cde2-11197d2e2-9156ae3-1038be3-12908ce3-7881de3+
     ------------------------------------------------------------------------
     11188e4 b4+7110a2c2-1742abc2-12249b2c2-7959ac3+6250bc3-7512c4+4970b3d-
     ------------------------------------------------------------------------
     14831a2cd+6357abcd-10793b2cd+14435ac2d-6885bc2d-4261c3d-13827a2d2+
     ------------------------------------------------------------------------
     11737abd2-15895b2d2+6684acd2+1488bcd2+5868c2d2+9025ad3-9711bd3+12204cd3+
     ------------------------------------------------------------------------
     5117d4-10875b3e-15875a2ce+13260abce+13964b2ce-14260ac2e+7766bc2e-572c3e+
     ------------------------------------------------------------------------
     6542a2de-12286abde-2722b2de-7451acde-14908bcde-2257c2de-4361ad2e+
     ------------------------------------------------------------------------
     12592bd2e+15731cd2e+4954d3e-13644a2e2+11272abe2+14744b2e2-3441ace2-
     ------------------------------------------------------------------------
     2674bce2-1864c2e2+2063ade2-394bde2-4906cde2-5482d2e2+4624ae3-11499be3+
     ------------------------------------------------------------------------
     15898ce3+9995de3+13616e4
     ------------------------------------------------------------------------
     abc3-3415b2c3+15032ac4-9163bc4-11054c5-4750a2c2d-2208abc2d+13641b2c2d+
     ------------------------------------------------------------------------
     646ac3d+14266bc3d+1014c4d-9036b3d2-4213a2cd2+11136abcd2+526b2cd2+
     ------------------------------------------------------------------------
     9850ac2d2-15509bc2d2+14988c3d2-11510a2d3+6468abd3+3072b2d3-10236acd3+
     ------------------------------------------------------------------------
     13289bcd3+3550c2d3+1271ad4+10962bd4+13537cd4+5193d5+13698a2c2e+
     ------------------------------------------------------------------------
     13334abc2e+3515b2c2e+11992ac3e-9434bc3e-4937c4e+11762b3de-5133a2cde-
     ------------------------------------------------------------------------
     10827abcde-11962b2cde+11598ac2de+8031bc2de-6089c3de-15199a2d2e+
     ------------------------------------------------------------------------
     13255abd2e+10822b2d2e+905acd2e-6053bcd2e-11580c2d2e-1585ad3e-8640bd3e+
     ------------------------------------------------------------------------
     7709cd3e-13926d4e+15370b3e2+14501a2ce2-13716abce2-13523b2ce2+11345ac2e2-
     ------------------------------------------------------------------------
     3210bc2e2-8734c3e2+3810a2de2+2094abde2+7680b2de2+14130acde2+736bcde2-
     ------------------------------------------------------------------------
     7016c2de2+11775ad2e2-7236bd2e2-11680cd2e2-5740d3e2+15981a2e3+8793abe3-
     ------------------------------------------------------------------------
     2490b2e3+10390ace3+7461bce3-15910c2e3+1926ade3+5716bde3+9737cde3-
     ------------------------------------------------------------------------
     12555d2e3+5992ae4+7157be4-10173ce4+7063de4-14617e5
     ------------------------------------------------------------------------
     a2c3+12993b2c3+6203ac4-1823bc4+7109c5+6532a2c2d-12631abc2d-9976b2c2d-
     ------------------------------------------------------------------------
     8117ac3d-12539bc3d+3652c4d+9273b3d2+2861a2cd2-12911abcd2+5657b2cd2-
     ------------------------------------------------------------------------
     14727ac2d2-13364bc2d2+10093c3d2+11554a2d3-5513abd3+10581b2d3+9690acd3-
     ------------------------------------------------------------------------
     11120bcd3-12690c2d3-7253ad4-507bd4-9410cd4+4650d5-15436a2c2e+3636abc2e-
     ------------------------------------------------------------------------
     13454b2c2e+9532ac3e+4058bc3e+14775c4e+7935b3de-3158a2cde-2764abcde-
     ------------------------------------------------------------------------
     11754b2cde-7637ac2de+2876bc2de-5888c3de+3671a2d2e+3761abd2e+2410b2d2e+
     ------------------------------------------------------------------------
     6015acd2e+15490bcd2e-5902c2d2e+11358ad3e+14213bd3e+10365cd3e-13287d4e+
     ------------------------------------------------------------------------
     9549b3e2-8869a2ce2+8079abce2-14436b2ce2+9549ac2e2+15592bc2e2+15598c3e2+
     ------------------------------------------------------------------------
     183a2de2+9289abde2+3455b2de2-12910acde2-459bcde2-13755c2de2-6770ad2e2-
     ------------------------------------------------------------------------
     9390bd2e2+2508cd2e2-8384d3e2+15310a2e3-8285abe3+9025b2e3+12968ace3+
     ------------------------------------------------------------------------
     13592bce3-6904c2e3-1644ade3-4139bde3-638cde3-15179d2e3+8567ae4+179be4-
     ------------------------------------------------------------------------
     6111ce4-5115de4+5990e5 |

             1       7
o6 : Matrix R  <--- R
i7 : leadTerm gbSnapshot(I)

o7 = | ab2 a2b a3 b3c b4 abc3 a2c3 |

             1       7
o7 : Matrix R  <--- R